Wave filter



Aug. 8, 1933. w R MAS N 1,921,035

WAVE FILTER Filed Sept. 30, 1931 2 Sheets-Sheet l REACTANCE mi {Wm CA Q INVENTOR W I? MASON yaw M A 7' TORNE'Y Aug. 8, 1933.

REACT/INCL OR ATTENUAT/ON FIG. 6

Filed Sept. 30, 1951 I I I I w. P. MASON 1,921,035

WAVE FILTER 2 Sheets-Sheet 2 FREQUENCY REACMNCE OR ATTE/VUAT/ON INVENTOR W R MASON ATTORNEY Patented Aug. 8, 1933 WAVE FILTER Warren P. Mason, East Orange, N. 3., assignor to Eell Telephone Laboratories, Incorporated, New York, N. IL, a Corporation of New York Application September 30, 1931 Serial No. 566,031

Claims.

This invention relates to broad band Wave filters in which piezo-electric crystals are used impedance elements and more particularly to crystal filters oi the low-pass type and of the high-pass type which are characterized by a single attenuation range and a single transmission range.

In my copending application, Serial No. 489,268, filed October 17, 1930, it is pointed out that in filters using piezo-electric crystals alone it is possible to obtain only very narrow transmission bands. For quartz crystals the maximum obtainable band width is about 0.7 per cent of the mean band frequency. In the same application filter networks are described in which by using piezo-electric crystals in combination with electrical inductances and capacities very much broader bands are obtained without impairing the sharp selectivity which is characteristic of piezo-electric crystals.

In accordance with the present invention piezoelectric crystal filters are provided in which the transmission band is so widened that one of the attenuation ranges is eliminated, the resulting transmission characteristic being either of the low-pass type or of the high-pass type.

The general form of the filters of the invention is similar to that of the filters described in my above mentioned copending application in that the crystal elements are combined with electrical inductances and capacities and that the branches of the networks are disposed in a symmetrical lattice formation.

The nature of the invention will be more fully apprehended from the following detailed description of networks representing typical embodiments thereof and by reference to the accompanying drawings of which:

Fig. 1 illustrates a form of crystal suitable for use in the networks of the invention;

Figs. 2 and 3 are diagrams illustrating the principles of the invention;

Fig. 4 shows schematically a low-pass filter embodying the invention;

Figs. 5 and 6 are diagrams illustrating the properties of the filter of Fig. 4;

Fig. 7 shows schematically a high-pass filter embodying the invention; and

Figs. 8 and 9 are diagrams illustrating the properties of the filter of Fig. 7.

The form and the cut of a crystal suitable for use in the frequency range up to about 500 kilocycles per second is shown in Fig. l in which 10 represents a crystal plate, preferably of quartz, having its length I parallel to the mechanical axis Min, its width w parallel to the optical axis 00', and its thickness t parallel to the electrical axis Electrodes 11 and 12 are applied to the large faces of the crystal preferably by the electrical deposition of a layer of silver or other metal to secure an intimate contact over the whole surface. Leads 13 and 14 are connected to the electrodes by soldering.

If the length of the crystal is great in comparison with the width, its electrical impedance for frequencies up to and well above the first resonance is of a simple character and corresponds to that of the electrical circuit shown in Fig. 2. Other resonances, representing changes in the mode of vibration are practically eliminated if the length is made about three times as great as the Width.

The equivalent electrical circuit, as shown in Fig. 2, comprises a parallel branch network between terminals 13 and 14, one branch consisting of an inductance La in series with a capacity Ca and ie other branch comprising a simple capacity Cb. For a quartz crystal of the type shown in Fig. l the values of the elements of the equivalent electrical circuit are given in terms of the crytal dimensions measured in centimeters by the following formula:

Henries,

C Farads, 1.

C F arads,

The capacity Cb is the simple electrostatic capacity between the electrodes and its value is independent of the piezo-electric effect. Inductance La and capacity Ca have values depending not only upon the crystal dimensions but also upon its piece-electric and elastic constants. These elements represent the piezo-electric property of the crystal. Capacity Cb is 140 times as great as capacity Ca and, except at frequencies close to the resonance of La and Ca, is the dominating factor in the crystal impedance.

Fig. 3 shows a typical crystal impedance characteristic and also shows the effect of combining a small inductance with the crystal. In this figure the curves show the variation of reactance, plotted as ordinates, with frequency, plotted as abscissa. The heavy line curve 15 represents the impedance of a crystal alone; dotted line curve 10 illustrates the impedance obtained by adding a small inductance in series with the crystal; and the light line curve 17 represents the impedance obtained with the same small inductance in parallel with the crystal. The reactance of the added inductance is represented by straight line 18.

For the crystal alone the impedance is characterized by a resonance frequency fa, and an antiresonance frequency is which is slightly higher. The values of fa and is in terms of the crystal dimensions are given by the following equations which are readily obtainable from the values given by Equation 1:

The extremely small separation of the two frequencies is due to the high ratio of Cb to 0.1.

The addition of a small inductance in series has the effect of moving the resonance frequency down to a slightly lower value, indicated by jc in the figure, introducing a new resonance frequency is at a considerably higher frequency. When the inductance is added in parallel the impedance exhibits anti-resonances at fs and is together with an intermediate resonance at the original frequency fa. If the added inductance is varied in magnitude, the upper frequency fa is shifted a large amount while the lower frequency is is not greatly altered. Likewise if capacity is added in parallel with on the upper frequency fa is moved closer to the crystal resonance while the lower frequency fc is not greatly affected.

The application of the foregoing principles to the design of a low-pass filter of the type shown schematically in Fig. -i will now be considered. In this figure a lattice type network is shown the line branches of which contain similar crystals Q1 shunted by adjustable capacities CA and the lattice branches of which contain similar crystals Q2 shunted by inductances L1 and adjustable cae capcities C13. The equivalent electrical circuit is shown in Fig. 5 wherein the resonant circuits L2C2 and L303 correspond to the crystal resonances of Q1 and Q2 respectively, Co represents the cornbination of CA with the electrode capacity of crystal Q1 and C1 represents the corresponding combinations for crystal Q2.

Fig. 6 shows certain characteristics of the filter of Fig. i and illustrates the requirements that must be met in order that the low-pass characteristic may be obtained. In this figure curves 19 and 20 represent the reactance-frequency characteristics of the line and the lattice branches respectively and curve 21 is a typical attenuationfrequency characteristic. The impedance of the line branches, comprising crystals Q1 and shunt capacities CA, is similar to that of a crystal alone, being characterized by a single resonance at frequency f1 and a single anti-resonance frequency is. The effect of the added capacity is simply to move the antiresonance frequency closer to the resonance frequency; in general, it is desirable that the added shunt capacity in the line branches should be small.

The formation of a single low-pass band requires that the impedance of the shunt branches should be of opposite sign to that of the line branches at all frequencies below the cut-off and of the same sign at all fr quencies above the cut-off. If the crystals of the lattice branches are so proportioned as to have their piezo-electric resonances at the frequency f2 and if they are shunted by small inductances an impedance characteristic for the lattice branches like curve 20' can be obtained and by proper proportioning of the inductance an anti-resonance can be produced at the frequency ii at which the line branch crystals are resonant. A second antiresonance of the lattice branches occurs at a higher frequency f3 which, as inspection of the diagram shows, becomes the filter cut-01f frequency.

In order that the cut-off may be sharp, it is desirable that the crystal resonances should be quite close to the cut-off frequency. From Fig. 3 it is seen that the addition of a small shunt inductance alone to a crystal tends to place the second anti-resonance frequency some distance above the crystal resonance; however, as explained in connection with Fig. 3 the further addition of a shunt capacity brings this frequency quite close to the crystal resonance without substantially affecting the position of the first antiresonance. By the proper choice of the shunt ing inductance and the shunting capacity, which, if desired, may be made empirically with the help of calculated impedance curves, the cut-off frequency may be brought as close as desired to the crystal resonances. A further control of the adjustment is provided by the small capacities CA shunting the line branch crystals.

In Fig. 6 the two reactance curves 19 and 20 are shown crossing at three points above the cut-off frequency, the crossing frequencies being designated by X1, X2 and X3, respectively. Since the lattice corresponds to a bridge network which is balanced when the branch impedances are equal, these frequencies correspond to points of infinite attenuation and in the particular case illustrated give rise to an attenuation characteristic of the type shown by curve 20. Various conditions are possible; for example, if the total shunting capacity C1 in the lattice branches is much smaller than the corresponding capacity Co of the line branches the curves may not cross at all and the attenuation characteristic would then have no peaks. This, however, would only occur in a filter having a cut-off considerably above the crystal resonances and would represent a case in whi h the crystals contribute little to the filter selectivity. In the type where the cutofi is brought close to the crystal resonances by the addition of shunt capacity to the lattice branches there will generally be three peaks as illustrated.

To develop explicit formulae for the design of a filter of this type, it is necessary that a sufficient number of parameters be specified. The most fundamental design paramters are the cut-off frequency and the characteristic impedance at zero frequency, but if these alone are specified a wide range of designs is possible which vary in respect of their attenuation characteristics or their phase characteristics in the transmission band. If the three frequencies of infinite attenuation are specified in addition to the cut-off frequency and the characteristic impedance, the design becomes fixed and explicit formulae for the elements can be found. Such formulae do not give the crystal dimensions directly but give the values of the various inductances and capacities indicated in Fig. 5 from which the crystal dimensions may be computed by means of equation 1.

The following formula, which may he arrived at by the same general procedure as is described in my aforementioned copending application in connection with the design of band pass filters,

in aca =\/&'% n=1, 2, 3,

I0 is the cut-off frequency, and

Z0 is the characteristic impedance at zero frequency.

In using these formulae it may be found that the choice of the peak frequencies X1 X2 and X3 gives rise to designs which are not physically realizable by means of crystals due to the fact that the capacities C0 and C1 are less than about 140 times the capacities C2 and C3 respectively. This limits the choice of the peak frequencies, but it is a simple matter to make a preliminary check by computing the capacity ratios for a given choice of peak frequencies before proceeding with the detail calculations. The capacity ra tios are given by So long as these ratios exceed 140 the filter will be physically realizable. As a general rule the peak frequencies should be quite close to the cutoff frequency, preferably all within two per cent.

A high-pass filter in accordance with the invention is shown schematically in Fig. 7. The same notation is used in this figure as in Fig. 4, the difference between the two circuits being that the added inductances L1 are connected in series with the latice branch crystals instead of in shunt therewith. The equivalent electrical circuit is shown in Fig. 8 in which, as in Fig. 5, the capacities Co and C1 represent the combinations of the added capacities CA and CB with the crystal electrode capacities.

The effect of adding an inductance in series with a crystal has already been described in connection with Fig. 3. If the added inductance is small the new resonance introduced by the inductance may be located a frequency considerably above the anti-resonance frequency while the lower resonance of the combination will be very little below the crystal resonance. The further addition of capacity in shunt to the crystal has the effect of bringing the upper resonance much closer to the crystal anti-resonance without substantiallyaffecting the position of the lower resonance.

The formation of a high-pass band with a network of the type shown in Fig. '7 is illustrated by the curves of Fig. 9 which show the required variation of the two branch impedances and'the type of attenuation characteristic obtained. Curve 22 corresponds to the reactance of the line branch impedances comprising crystals Q1 and shunting capacities CA. Curve 23 corresponds to the lattice branch impedances comprising crystals Q2 shunted by capacities CB and having inductances L1 in series. The line branch impedances are resonant at a frequency f2 and anti-resonant at a slightly higher frequency 3. The lattice branches are resonant at a frequency f1 lower than f2 and are anti-resonant and resonant at frequencies f2 and f3 respectively. Above h which is the cut-off of the filter the impedances are always of opposite sign indicating a transmission band, while below f1 they are of the same sign indicating an attenuation band.

Below the cut-off frequency the reactance curves cross at points corresponding to three frequencies X1, X2 and X3 at which, as pointed out in connection with Fig. 6, the attenuation of the filter becomes infinite. This is illustrated by curve 24 in which the ordinates representattenuation. The adjustment of :thecrystal dimensions and those of the associated electrical impedances may be accomplished in the empirical manner indicated in connection with the design of a lowpass filter or the frequencies of infinite attenuation may be used as design parameters for the development of explicit design formulae. As in the case of the low-pass filter, the three crossing frequencies are obtained when a relatively large capacity is used to shunt the lattice branch crystals, this also being the condition that brings all of the critical frequencies close to the cut-off.

The following formula: apply to the design of a high-pass filter of the type shown in Figs. 7 and 8:

Zn 21am in which:

B: b1b2+ 2 3+ ii la D=b1b2b3,

preliminarycheck on the valuesassumed for X1, X2 and 22 to insure that the capacity ratios 2 and 3 I have values greater than 140, this being the requirement that the circuit may be physically realizable when crystals are used. The requirement is best met by placing all three of the peak frequencies very close to the cut-off frequency.

What is claimed is:

1. A broad band wave filter network comprising four impedance branches equal in pairs and disposed to form a symmetrical lattice, one of said pairs of branches including similar piezoelectric crystals in combination with equal inductances and the other of said branches including similar piezo-electric crystals and having impedances adjusted with respect to the impedances of the first pair of branches to provide a single transmission band of frequencies and a single attenuation band.

2. A broad band wave filter network comprising four impedance branches equal in pairs and disposed to form a symmetrical lattice, one of said pairs of branches comprising similar piezoelectric crystals and equal inductances connected in parallel and the others of said branches including similar piezo-electric crystals and having impedances proportioned with respect to the impedances of the first pair of branches to provide a transmission band extending from zero to a finite frequency.

3. A wave filter in accordance with claim 2 in which the branches including the shunting inductances include also shunting capacities whereby the filter cut-off frequency is brought close to the resonance frequency of the shunted crystals.

4. A broad band wave filter network comprising four impedance branches equal in pairs and disposed to form a symmetrical lattice, one of said pairs of branches comprising similar piezoelectric crystals and equal inductances connected in series and the others of said branches comprising similar piezo-electric crystals and having impedances proportioned with respect to the impedances of the first pair of branches to provide a single attenuation band extending from zero to a finite frequency and a single transmission band.

5. A wave filter in accordance with claim 4 in which the branches including the series inductances include also capacities in shunt to the crystals whereby the filter cut-off frequency is brought close to the resonance frequency of the crystals.

WARREN P. MASON. 

